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ΓL(1,𝔽8)×Dic365 #44501275

order30660
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×Dic365

Splittings

derived, HallC5×C7×C73 ⋊ C3×C4
HallC7×Dic365 ⋊ C3
HallC5×ΓL(1,𝔽8)×C73 ⋊ C4
HallΓL(1,𝔽8)×C73 ⋊ Dic5
HallC7×C73 ⋊ C3×Dic5
HallC5×C73 ⋊ C4×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ Dic73
SylowC73 ⋊ Dic5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic73
SylowC7 ⋊ C3×Dic365
SylowC5 ⋊ ΓL(1,𝔽8)×Dic73

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D365
commutator, hypocenterC5×C7×C73C3×C4
Fitting, socle, cosocleC2×C5×C7×C73C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C73C2
LCSG ▷ C5×C7×C73
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 38);